Find a rational function that has vertical asymptotes x=-1 and x=2 and x-intercept (-4,0)

Question

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Answer 1

A vertical asymptote usually occurs when we get division by zero. This suggests that when x=-1 we have a zero in the denominator, that is, we have an expression divided by x+1, and by x-2, because we get zero for x=-1 and 2. So it looks like f(x)/((x+1)(x-2)). We also have an x intercept at (-4,0), which means when x=-4, y is zero. So perhaps f(x)=x+4 and a possible function is (x+4)/((x+1)(x-2)).

This can be expressed in partial fractions: 2/(x-2)-1/(x+1).